# On the null energy condition in scale dependent frameworks with spherical symmetry

## TL;DR

This paper explores how a scale-dependent Newton coupling, relevant in quantum gravity, affects non-rotating black holes and demonstrates it can be derived without solving complex quantum equations using the null energy condition.

## Contribution

It introduces a method to determine the scale-dependent Newton coupling in black holes without solving quantum gap equations, using the null energy condition.

## Key findings

- Newton's scale-dependent coupling can be obtained without quantum gap equations.
- The approach applies to non-rotating black holes.
- The null energy condition constrains the scale dependence of gravity.

## Abstract

The effect of a scale dependent newton coupling, which is a crucial ingredient of many quantum gravity theories, is investigated in this paper. For case of non-rotating black holes, and using the null energy condition, we show that Newtons scale dependent coupling can actually be obtained without solving the full quantum gap equations.